/* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================
 
 Copyright (C) 2002-2012 Yves Renard, Julien Pommier
 
 This file is a part of GETFEM++
 
 Getfem++  is  free software;  you  can  redistribute  it  and/or modify it
 under  the  terms  of the  GNU  Lesser General Public License as published
 by  the  Free Software Foundation;  either version 3 of the License,  or
 (at your option) any later version along with the GCC Runtime Library
 Exception either version 3.1 or (at your option) any later version.
 This program  is  distributed  in  the  hope  that it will be useful,  but
 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
 or  FITNESS  FOR  A PARTICULAR PURPOSE.  See the GNU Lesser General Public
 License and GCC Runtime Library Exception for more details.
 You  should  have received a copy of the GNU Lesser General Public License
 along  with  this program;  if not, write to the Free Software Foundation,
 Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301, USA.
 
 As a special exception, you  may use  this file  as it is a part of a free
 software  library  without  restriction.  Specifically,  if   other  files
 instantiate  templates  or  use macros or inline functions from this file,
 or  you compile this  file  and  link  it  with other files  to produce an
 executable, this file  does  not  by itself cause the resulting executable
 to be covered  by the GNU Lesser General Public License.  This   exception
 does not  however  invalidate  any  other  reasons why the executable file
 might be covered by the GNU Lesser General Public License.
 
===========================================================================*/

/**@file getfem_derivatives.h
   @author Yves Renard <Yves.Renard@insa-lyon.fr>,
   @author Julien Pommier <Julien.Pommier@insa-toulouse.fr>
   @date June 17, 2002.
   @brief Compute the gradient of a field on a getfem::mesh_fem.
*/
#ifndef GETFEM_DERIVATIVES_H__
#define GETFEM_DERIVATIVES_H__

#include "getfem_mesh_fem.h"
#include "getfem_interpolation.h"
#include "gmm/gmm_dense_qr.h"

namespace getfem
{
  /** Compute the gradient of a field on a getfem::mesh_fem.
      @param mf the source mesh_fem.
      @param U the source field.
      @param mf_target should be a lagrange discontinous element
      does not work with vectorial elements. ... to be done ...
      @param V contains on output the gradient of U, evaluated on mf_target.

      mf_target may have the same Qdim than mf, or it may
      be a scalar mesh_fem, in which case the derivatives are stored in
      the order: DxUx,DyUx,DzUx,DxUy,DyUy,...

      in any case, the size of V should be
      N*(mf.qdim)*(mf_target.nbdof/mf_target.qdim)
      elements (this is not checked by the function!)
  */
  template<class VECT1, class VECT2>
  void compute_gradient(const mesh_fem &mf, const mesh_fem &mf_target,
                        const VECT1 &UU, VECT2 &VV) {
    typedef typename gmm::linalg_traits<VECT1>::value_type T;

    size_type N = mf.linked_mesh().dim();
    size_type qdim = mf.get_qdim();
    size_type target_qdim = mf_target.get_qdim();
    size_type qqdimt = qdim * N / target_qdim;
    std::vector<T> U(mf.nb_basic_dof());
    std::vector<T> V(mf_target.nb_basic_dof() * qqdimt);

    mf.extend_vector(UU, U);

    GMM_ASSERT1(&mf.linked_mesh() == &mf_target.linked_mesh(),
                "meshes are different.");
    GMM_ASSERT1(target_qdim == qdim*N || target_qdim == qdim
		|| target_qdim == 1, "invalid Qdim for gradient mesh_fem");
    
    base_matrix G;
    std::vector<T> coeff;
 
    bgeot::pgeotrans_precomp pgp = NULL;
    pfem_precomp pfp = NULL;
    pfem pf, pf_target, pf_old = NULL, pf_targetold = NULL;
    bgeot::pgeometric_trans pgt;

    for (dal::bv_visitor cv(mf_target.convex_index()); !cv.finished(); ++cv) {
      pf = mf.fem_of_element(cv);
      pf_target = mf_target.fem_of_element(cv);
      if (!pf) continue;
      
      GMM_ASSERT1(!(pf_target->need_G()) && pf_target->is_lagrange(),
                  "finite element target not convenient");
      
      bgeot::vectors_to_base_matrix(G, mf.linked_mesh().points_of_convex(cv));

      pgt = mf.linked_mesh().trans_of_convex(cv);
      if (pf_targetold != pf_target) {
        pgp = bgeot::geotrans_precomp(pgt, pf_target->node_tab(cv), pf_target);
      }
      pf_targetold = pf_target;

      if (pf_old != pf) {
        pfp = fem_precomp(pf, pf_target->node_tab(cv), pf_target);
      }
      pf_old = pf;

      gmm::dense_matrix<T> grad(N,qdim), gradt(qdim,N);
      fem_interpolation_context ctx(pgp,pfp,0,G,cv, size_type(-1));
      slice_vector_on_basic_dof_of_element(mf, U, cv, coeff);
      // gmm::resize(coeff, mf.nb_basic_dof_of_element(cv));
      // gmm::copy(gmm::sub_vector
      //          (U, gmm::sub_index(mf.ind_basic_dof_of_element(cv))), coeff);
      for (size_type j = 0; j < pf_target->nb_dof(cv); ++j) {
        size_type dof_t =
          mf_target.ind_basic_dof_of_element(cv)[j*target_qdim] * qqdimt;
        ctx.set_ii(j);
        pf->interpolation_grad(ctx, coeff, gradt, dim_type(qdim));
        gmm::copy(gmm::transposed(gradt),grad);
        std::copy(grad.begin(), grad.end(), V.begin() + dof_t);
      }
    }

    mf_target.reduce_vector(V, VV);
  }

  /** Compute the hessian of a field on a getfem::mesh_fem.
      @param mf the source mesh_fem.
      @param U the source field.
      @param mf_target should be a lagrange discontinous element
      does not work with vectorial elements. ... to be done ...
      @param V contains on output the gradient of U, evaluated on mf_target.

      mf_target may have the same Qdim than mf, or it may
      be a scalar mesh_fem, in which case the derivatives are stored in
      the order: DxxUx,DxyUx, DyxUx, DyyUx, ...

      in any case, the size of V should be
      N*N*(mf.qdim)*(mf_target.nbdof/mf_target.qdim)
      elements (this is not checked by the function!)
  */
  template<class VECT1, class VECT2>
  void compute_hessian(const mesh_fem &mf, const mesh_fem &mf_target,
                        const VECT1 &UU, VECT2 &VV) {
    typedef typename gmm::linalg_traits<VECT1>::value_type T;

    size_type N = mf.linked_mesh().dim();
    size_type qdim = mf.get_qdim();
    size_type target_qdim = mf_target.get_qdim();
    size_type qqdimt = qdim * N * N / target_qdim;
    std::vector<T> U(mf.nb_basic_dof());
    std::vector<T> V(mf_target.nb_basic_dof() * qqdimt);

    mf.extend_vector(UU, U);

    GMM_ASSERT1(&mf.linked_mesh() == &mf_target.linked_mesh(),
                "meshes are different.");
    GMM_ASSERT1(target_qdim == qdim || target_qdim == 1,
                "invalid Qdim for gradient mesh_fem");
    base_matrix G;
    std::vector<T> coeff;
 
    bgeot::pgeotrans_precomp pgp = NULL;
    pfem_precomp pfp = NULL;
    pfem pf, pf_target, pf_old = NULL, pf_targetold = NULL;
    bgeot::pgeometric_trans pgt;

    for (dal::bv_visitor cv(mf_target.convex_index()); !cv.finished(); ++cv) {
      pf = mf.fem_of_element(cv);
      pf_target = mf_target.fem_of_element(cv);
      GMM_ASSERT1(!(pf_target->need_G()) && pf_target->is_lagrange(),
                  "finite element target not convenient");
      
      bgeot::vectors_to_base_matrix(G, mf.linked_mesh().points_of_convex(cv));

      pgt = mf.linked_mesh().trans_of_convex(cv);
      if (pf_targetold != pf_target) {
        pgp = bgeot::geotrans_precomp(pgt, pf_target->node_tab(cv), pf_target);
      }
      pf_targetold = pf_target;

      if (pf_old != pf) {
        pfp = fem_precomp(pf, pf_target->node_tab(cv), pf_target);
      }
      pf_old = pf;

      gmm::dense_matrix<T> hess(N*N,qdim), hesst(qdim,N*N);
      fem_interpolation_context ctx(pgp,pfp,0,G,cv, size_type(-1));
      slice_vector_on_basic_dof_of_element(mf, U, cv, coeff);      
      // gmm::resize(coeff, mf.nb_basic_dof_of_element(cv));
      // gmm::copy(gmm::sub_vector
      //          (U, gmm::sub_index(mf.ind_basic_dof_of_element(cv))), coeff);
      for (size_type j = 0; j < pf_target->nb_dof(cv); ++j) {
        size_type dof_t
          = mf_target.ind_basic_dof_of_element(cv)[j*target_qdim] * qqdimt;
        ctx.set_ii(j);
        pf->interpolation_hess(ctx, coeff, hesst, dim_type(qdim));
        gmm::copy(gmm::transposed(hesst), hess);
        std::copy(hess.begin(), hess.end(), V.begin() + dof_t);
      }
    }

    mf_target.reduce_vector(V, VV);
  }

  /**Compute the Von-Mises stress of a field (only valid for
     linearized elasticity in 3D)
  */
  template <typename VEC1, typename VEC2>
  void interpolation_von_mises(const getfem::mesh_fem &mf_u, 
                               const getfem::mesh_fem &mf_vm, 
                               const VEC1 &U, VEC2 &VM,
                               scalar_type mu=1) {
    dal::bit_vector bv; bv.add(0, mf_vm.nb_dof());
    interpolation_von_mises(mf_u, mf_vm, U, VM, bv, mu);
  }

  template <typename VEC1, typename VEC2>
  void interpolation_von_mises(const getfem::mesh_fem &mf_u, 
                               const getfem::mesh_fem &mf_vm, 
                               const VEC1 &U, VEC2 &VM,
                               const dal::bit_vector &mf_vm_dofs,
                               scalar_type mu=1) {

    assert(mf_vm.get_qdim() == 1); 
    unsigned N = mf_u.linked_mesh().dim(); assert(N == mf_u.get_qdim());
    std::vector<scalar_type> DU(mf_vm.nb_dof() * N * N);
    
    getfem::compute_gradient(mf_u, mf_vm, U, DU);
    
    GMM_ASSERT1(!mf_vm.is_reduced(), "Sorry, to be done");

    scalar_type vm_min, vm_max;
    for (dal::bv_visitor i(mf_vm_dofs); !i.finished(); ++i) {
      VM[i] = 0;
      scalar_type sdiag = 0.;
      for (unsigned j=0; j < N; ++j) {
        sdiag += DU[i*N*N + j*N + j];
        for (unsigned k=0; k < N; ++k) {
          scalar_type e = .5*(DU[i*N*N + j*N + k] + DU[i*N*N + k*N + j]);
          VM[i] += e*e; 
        }
      }
      VM[i] -= 1./N * sdiag * sdiag;
      vm_min = (i == 0 ? VM[0] : std::min(vm_min, VM[i]));
      vm_max = (i == 0 ? VM[0] : std::max(vm_max, VM[i]));
    }
    cout << "Von Mises : min=" << 4*mu*mu*vm_min << ", max="
         << 4*mu*mu*vm_max << "\n";
    gmm::scale(VM, 4*mu*mu);
  }
  

  /** Compute the Von-Mises stress of a field (valid for
      linearized elasticity in 2D and 3D)
  */
  template <typename VEC1, typename VEC2, typename VEC3>
  void interpolation_von_mises_or_tresca(const getfem::mesh_fem &mf_u, 
                                         const getfem::mesh_fem &mf_vm, 
                                         const VEC1 &U, VEC2 &VM,
                                         const getfem::mesh_fem &mf_lambda,
                                         const VEC3 &lambda, 
                                         const getfem::mesh_fem &mf_mu,
                                         const VEC3 &mu,
                                         bool tresca) {
    assert(mf_vm.get_qdim() == 1);
    typedef typename gmm::linalg_traits<VEC1>::value_type T;
    size_type N = mf_u.get_qdim();
    std::vector<T> GRAD(mf_vm.nb_dof()*N*N), 
      LAMBDA(mf_vm.nb_dof()), MU(mf_vm.nb_dof());
    base_matrix sigma(N,N);
    base_vector eig(N);
    if (tresca) interpolation(mf_lambda, mf_vm, lambda, LAMBDA);
    interpolation(mf_mu, mf_vm, mu, MU);
    compute_gradient(mf_u, mf_vm, U, GRAD);

    GMM_ASSERT1(!mf_vm.is_reduced(), "Sorry, to be done");
    GMM_ASSERT1(N>=2 && N<=3, "Only for 2D and 3D");
    
    for (size_type i = 0; i < mf_vm.nb_dof(); ++i) {
      scalar_type trE = 0, diag = 0;
      for (unsigned j = 0; j < N; ++j)
        trE += GRAD[i*N*N + j*N + j];
      if (tresca)
        diag = LAMBDA[i]*trE; // calculation of sigma
      else
        diag = (-2./3.)*MU[i]*trE;  // for the calculation of deviator(sigma)
      for (unsigned j = 0; j < N; ++j) {
        for (unsigned k = 0; k < N; ++k) {
          scalar_type eps = /* 0.5* */ (GRAD[i*N*N + j*N + k] + 
                                        GRAD[i*N*N + k*N + j]);
          sigma(j,k) = /* 2* */ MU[i]*eps;
        }
        sigma(j,j) += diag;
      }
      if (!tresca) {
        /* von mises: norm(deviator(sigma)) */
        //gmm::add(gmm::scaled(Id, -gmm::mat_trace(sigma) / N), sigma); 
        if (N==3)
          VM[i] = sqrt((3./2.)*gmm::mat_euclidean_norm_sqr(sigma));
        else // for plane strains ( s_33 = -diag )
          VM[i] = sqrt((3./2.)*(gmm::mat_euclidean_norm_sqr(sigma) + diag*diag));
      } else {
        /* else compute the tresca criterion */
        gmm::symmetric_qr_algorithm(sigma, eig);
        std::sort(eig.begin(), eig.end());
        VM[i] = eig.back() - eig.front();
      }
    }
  }
}

#endif
